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Horocycle dynamics : new invariants and eigenform loci in the stratum H(1,1)
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Bainbridge, Matt, Smillie, John and Weiss, Barak (2020) Horocycle dynamics : new invariants and eigenform loci in the stratum H(1,1). Memoirs of the American Mathematical Society, 280 (1384). doi:10.1090/memo/1384 ISSN 0065-9266.
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Official URL: https://doi.org/10.1090/memo/1384
Abstract
We study dynamics of the horocycle flow on strata of translation surfaces, introduce new invariants for ergodic measures, and analyze the interaction of the horocycle flow and real Rel surgeries. We use this analysis to complete and ex- tend results of Calta and Wortman classifying horocycle-invariant measures in the eigenform loci. In addition we classify the horocycle orbit-closures and prove that every orbit is equidistributed in its orbit-closure. We also prove equidistribution results describing limits of sequences of measures. Our results have applications to the problem of counting closed trajectories on translation surfaces of genus 2.
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||
Library of Congress Subject Headings (LCSH): | Surfaces , Geometry, Hyperbolic, Hecke algebra, Invariant measures | |||||||||||||||
Journal or Publication Title: | Memoirs of the American Mathematical Society | |||||||||||||||
Publisher: | American Mathematical Society | |||||||||||||||
ISBN: | 9781470455392 | |||||||||||||||
ISSN: | 0065-9266 | |||||||||||||||
Official Date: | 7 October 2020 | |||||||||||||||
Dates: |
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Volume: | 280 | |||||||||||||||
Number: | 1384 | |||||||||||||||
DOI: | 10.1090/memo/1384 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Reuse Statement (publisher, data, author rights): | First published in Proceedings of the American Mathematical Society in [280/1384, 2022], published by the American Mathematical Society | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Date of first compliant deposit: | 1 July 2020 | |||||||||||||||
Date of first compliant Open Access: | 1 July 2020 | |||||||||||||||
RIOXX Funder/Project Grant: |
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